Find the Exact Value cos(420)

Problem

cos(420^∘)

Solution

1. Find the coterminal angle by subtracting 360^∘ from the given angle to bring it within the standard range of 0^∘ to 360^∘

420^∘−360^∘=60^∘

2. Identify the quadrant for the angle 60^∘ which is in the first quadrant where all trigonometric functions are positive.

cos(420^∘)=cos(60^∘)

3. Determine the exact value using the unit circle or special right triangles (30^∘−60^∘−90^∘.

cos(60^∘)=1/2

Final Answer

cos(420^∘)=1/2

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